Ever since Michael Behe published Darwin’s Black Box in 1996, the concept of irreducible complexity has played a central role in the debate over Darwinian theory. I am proposing a new, theoretical method of determining whether a system is irreducibly complex using power-sets. First, however, it is necessary to define irreducible complexity.
Various definitions of irreducible complexity exist. Michael Behe defines it as “a single system which is composed of several interacting parts, and where the removal of any one of the parts causes the system to cease functioning.” Critics have noted that this definition is actually a definition of interlocking complexity, a concept H. J. Muller had written about years earlier and which is perfectly compatible with Darwinian theory. In this article, I will be using the definition provided by Charles Darwin himself. Although the term did not exist in Darwin’s day, the concept was foreseen; it was, moreover, readily acknowledged that any example of an irreducibly complex system would break down Darwinian theory. According to Darwin: “If it could be demonstrated that any complex organ existed, which could not possibly have been formed by numerous, successive, slight modifications, my theory would absolutely break down.” In the following paragraph, he follows this by warning, “We should be extremely cautious in concluding that an organ could not have been formed by transitional gradations of some kind.” It would, indeed, be ridiculous to rule out evolutionary explanations simply because we don’t know how they evolved; these explanations may be put in doubt, but they could not be ruled out absolutely. Thus, in the scientific search for irreducible complexity it is imperative that scientists be meticulous in considering every possible slight modification. It is only if all possibilities for a given evolutionary gradation would break down the system, either being physically impossible without the other parts, or otherwise harmful to the organism, that it can be said with certainty that the system in question is irreducibly complex and could not, therefore, have been the result of evolution alone.
I am proposing power-sets as a method which may be used to approach the issue. The veracity of this approach, however, must be tested by other scientists. I am convinced, currently, that the use of power-sets for biological systems can allow for the reasonable assessment of these systems as irreducibly complex. A power-set is the set of all possible subsets for a given set. If all the parts of a system are known, a power-set of these parts can be made, and this power-set is all possible combinations of parts. This would allow scientists to determine all possibilities for an evolutionary gradation.
To illustrate this, I will be using Behe’s example of the flagellum and apply this method to it. This is a thought experiment, intended to demonstrate how one might use this method, and so I will not be considering all parts of the flagellum. Since I am not trying to argue for the irreducible complexity of the flagellum here, that will not be necessary. If the most basic parts of the flagellum – filament, hook, and basal body – are put into the power-set equation, it looks like this:
- Basal body
- Filament, hook
- Filament, basal body
- Hook, basal body
- Filament, hook, basal body
In this very simplistic power-set, (7) is the final product, the flagellum; (1-3) are possible first modifications; (4-6) are possible second modifications. If (1-3) could not have evolved by themselves, or if (4-6) could not have evolved by themselves without breaking down the entire system, either being physically impossible or harmful to the organism, then it could be established with reasonable certainty that the flagellum is irreducibly complex. Of course, no accurate assessment could be made from considering these parts alone – all parts of the system would need to be taken into account. I am calling this the “Method for Determining Irreducible Complexity from Biological Power-sets.”